Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
540 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #23781561 | C2 | semidirect |
| 4. #23781556 | C2 | semidirect |
| 5. #23781527 | C2 | semidirect |
| 6. #23781524 | C2 | semidirect |
| 7. #23781511 | C2 | semidirect |
| 8. C4×C4⋊C4×C163 | C2 | semidirect |
| 11. C4×D652 | C4 | semidirect |
| 96. C163 | #2319 | semidirect |
| 104. C4×C4⋊C4 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D652 | 2 |
| #23781566 | 2 |
| #23781561 | 2 |
| #23781556 | 2 |
| #23781527 | 2 |
| #23781524 | 2 |
| #23781511 | 2 |
| C4×C4⋊C4×C163 | 2 |
| #2319 | 163 |